Study of two-body doubly charmful baryonic $B$ decays with $SU(3)$ flavor symmetry

Abstract: Within the framework of $SU(3)$ flavor symmetry, we investigate two-body doubly charmful baryonic $B\to{\bf B}c\bar{\bf B}'_c$ decays, where ${\bf B}_c\bar{\bf B}'_c$ represents the anti-triplet charmed dibaryon. We determine the $SU(3)_f$ amplitudes and calculate ${\cal B}(B^-\to \Xi_c^0\bar \Xi_c^-)=(3.4^{+1.0}{-0.9})\times 10^{-5}$ and ${\cal B}(\bar B^0_s\to \Lambda_c^+\bar \Xi_c^-)=(3.9^{+1.2}_{-1.0})\times 10^{-5}$ induced by the single $W$-emission configuration. We find that the $W$-exchange amplitude, previously neglected in studies, needs to be taken into account. It can cause a destructive interfering effect with the $W$-emission amplitude, alleviating the significant discrepancy between the theoretical estimation and experimental data for ${\cal B}(\bar B^0\to\Lambda_c^+\bar\Lambda_c^-)$. To test other interfering decay channels, we calculate ${\cal B}(\bar B^0_s\to \Xi_c^{0(+)}\bar \Xi_c^{0(+)})=(3.0^{+1.4}_{-1.1})\times 10^{-4}$ and ${\cal B}(\bar B^0\to \Xi_c^0\bar \Xi_c^0)=(1.5^{+0.7}_{-0.6})\times 10^{-5}$. We estimate non-zero branching fractions for the pure $W$-exchange decay channels, specifically ${\cal B}(\bar B^0_s\to \Lambda_c^+\bar \Lambda_c^-)=(8.1^{+1.7}_{-1.5})\times 10^{-5}$ and ${\cal B}(\bar B^0\to \Xi_c^+\bar \Xi_c^-)=(3.0\pm 0.6)\times 10^{-6}$. Additionally, we predict ${\cal B}(B^+_c\to \Xi_c^+\bar \Xi_c^0)=(2.8^{+0.9}_{-0.7})\times 10^{-4}$ and ${\cal B}(B^+_c\to \Lambda_c^+\bar \Xi_c^0)=(1.6^{+0.5}_{-0.4})\times 10^{-5}$, which are accessible to experimental facilities such as LHCb.